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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Closures of conjugacy classes in classical real linear Lie groups. II
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by Dragomir Ž. Djoković PDF
Trans. Amer. Math. Soc. 270 (1982), 217-252 Request permission

Abstract:

By a classical group we mean one of the groups $G{L_n}(R)$, $G{L_n}(C)$, $G{L_n}(H)$, $U(p, q)$, ${O_n}(C)$, $O(p, q)$, $S{O^{\ast }}(2n)$, $S{p_{2n}}(C)$, $S{p_{2n}}(R)$, or $Sp(p, q)$. Let $G$ be a classical group and $L$ its Lie algebra. For each $x \in L$ we determine the closure of the orbit $G \cdot x$ (for the adjoint action of $G$ on $L$). The problem is first reduced to the case when $x$ is nilpotent. By using the exponential map we also determine the closures of conjugacy classes of $G$.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 270 (1982), 217-252
  • MSC: Primary 22E15
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0642339-4
  • MathSciNet review: 642339